Floats on Mercury

1. The problem statement, all variables and given/known data
A 17.89 cm diameter, 42.43 cm tall steel cylinder (rsteel=7900 kg/m3) floats in mercury. The axis of the cylinder is perpendicular to the surface. What length of steel is above the surface?


2. Relevant equations

Pb=Pa+density*g*h


3. The attempt at a solution

Pa=101300
Pb?
density= 7900 kg/m^3
H=(total length-submerged)
g=(9.8)

Pb=101300+((9.8*7900*(total length-submerged))

I have 2 unkowns. What would Pb be?

 

Any help would be much apperiated!

 

For some reason I am having a hard time grasping pressure.

 

Will Pb(pressure on bottom) always equal the denisty * depth? That is the density of the force acting against the object in this case......mercury?

 

so i have RHO(mercury)*H(submerged)=101300(Pa)+(RHO*G*LENGTH OF CYLINDER)

solve for h i have (101300+(7900*9.8*.4243))/13600= 9.8 m.....?

 

i tried 0 seeing if it was a trick question but the trick was on me because it was wrong

 

So Pb= pressure on surface of mercury+denisty *g*h? that doesn't seem right

 

What doesn't seem right is that Pb is pressure at bottom, so why would i need the pressure at the top.
Pb=Pa+rho*g*h
^ ^
^ ^
^ Pressure at above which in this case is atmosphereic pressure
^
Pressure at bottom

So if the pressure at the bottom is just (density of mercury*h*g) that works right? Where h is the amount submerged

The pressure at the top/above is jsut 101300 Pa

rho is denisty of the stell which is given 7900, g is 9.8 and h is the total height

Where am I going wrong?

 

Isn't that why we have pressure above the can?

 

Is there another way to appoarch this?

 

I can use the density of steel to see how much steel is present, then this is also equal to the weight of displaced mercury. CORRECT?

Then see how deep it is using m=Vp. CORRECT?